Roast peppers on a baking sheet in the oven for 15 to 20 minutes, until the skins begin to blister. When the skins are fully blistered, remove the peppers from the oven, let them cool 2 to 3 minutes, and then cover with plastic wrap and let steam for 15 minutes. The steam will loosen the skin.

Remove plastic wrap and peel the skin. Chop peppers in half, discard seeds and dice peppers into strips. Let peppers drain in a colander for at least 15 minutes, tossing them occasionally to get out all the extra water.

In a food processor fitted with a metal blade, purée the peppers until they are smooth. The puréed peppers should measure 4 cups.

In a large mixing bowl, whisk together the eggs, egg yolks, cream, lemon juice, Gruyère, chives, chicken stock, sugar, Parmesan, melted butter, salt and black pepper until they are well blended. Stir in pepper purée until fully combined.

Turn the oven down to 325 degrees. Pour the mixture into a prebaked 9-by-13-inch tart shell and bake for 25 to 30 minutes, until slightly firm. Remove from oven and cool 15 minutes. Serve warm or cold.